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Simplifying (z + -2)(z + 2z + 4) = 0 Reorder the terms: (-2 + z)(z + 2z + 4) = 0 Reorder the terms: (-2 + z)(4 + z + 2z) = 0 Combine like terms: z + 2z = 3z (-2 + z)(4 + 3z) = 0 Multiply (-2 + z) * (4 + 3z) (-2(4 + 3z) + z(4 + 3z)) = 0 ((4 * -2 + 3z * -2) + z(4 + 3z)) = 0 ((-8 + -6z) + z(4 + 3z)) = 0 (-8 + -6z + (4 * z + 3z * z)) = 0 (-8 + -6z + (4z + 3z2)) = 0 Combine like terms: -6z + 4z = -2z (-8 + -2z + 3z2) = 0 Solving -8 + -2z + 3z2 = 0 Solving for variable 'z'. Factor a trinomial. (-4 + -3z)(2 + -1z) = 0Subproblem 1
Set the factor '(-4 + -3z)' equal to zero and attempt to solve: Simplifying -4 + -3z = 0 Solving -4 + -3z = 0 Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3z = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3z = 0 + 4 -3z = 0 + 4 Combine like terms: 0 + 4 = 4 -3z = 4 Divide each side by '-3'. z = -1.333333333 Simplifying z = -1.333333333Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve: Simplifying 2 + -1z = 0 Solving 2 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1z = 0 + -2 -1z = 0 + -2 Combine like terms: 0 + -2 = -2 -1z = -2 Divide each side by '-1'. z = 2 Simplifying z = 2Solution
z = {-1.333333333, 2}
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